Theorem ancomsd 265

Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004.)

Hypothesis

Ref	Expression
ancomsd.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Assertion

Ref	Expression
ancomsd	|- ( ph -> ( ( ch /\ ps ) -> th ) )

Proof of Theorem ancomsd

Step	Hyp	Ref	Expression
1		ancom 262	. 2 |- ( ( ch /\ ps ) <-> ( ps /\ ch ) )
2		ancomsd.1	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	1, 2	syl5bi 150	1 |- ( ph -> ( ( ch /\ ps ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  sylan2d  288  mpand  419  anabsi6  544  ralxfrd  4212  rexxfrd  4213  poirr2  4737  smoel  5938  genprndl  6711  genprndu  6712  addcanprlemu  6805  leltadd  7551  lemul12b  7939  lbzbi  8701  dvdssub2  10237